You get Zapdos same as in the Kanto games ( red, blue, yellow, fire red, leaf green), you get it at the power plant. The Power Plant is near Cerulean city or the "Rock Tunnel". You catch it outside the Power plant after you find the gear and give it back to the owner inside.
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Yes, all 3 of them (Articuno, Zapdos and Moltres) will be in Pokémon HeartGold and Pokémon SoulSilver.
You can only catch Zapdos in Crystal by cheating. otherwise it is not in the game
to catch zapdos in pokemon black you have to have every legendary pokemon
If you mean how to consider yourself as beaten the kanto region in pokemon soulsilver, then you should find zapdos,moltres, and articuno. You should also beat Red (Ash Ketchum). Once you do that, you can catch Mewtwo.
After you get the EXPN card he is right next to the Power Plant.